Nuprl Lemma : shorten-tuple_wf
∀[L:Type List]. ∀[n:ℕ||L||]. ∀[x:tuple-type(L)]. (shorten-tuple(x;n) ∈ tuple-type(nth_tl(n;L)))
Proof
Definitions occuring in Statement :
shorten-tuple: shorten-tuple(x;n),
tuple-type: tuple-type(L),
length: ||as||,
nth_tl: nth_tl(n;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
top: Top,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
shorten-tuple-split-tuple,
int_seg_subtype_nat,
length_wf,
false_wf,
pi2_wf,
tuple-type_wf,
firstn_wf,
nth_tl_wf,
split-tuple_wf,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
natural_numberEquality,
instantiate,
universeEquality,
hypothesis,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[L:Type List]. \mforall{}[n:\mBbbN{}||L||]. \mforall{}[x:tuple-type(L)]. (shorten-tuple(x;n) \mmember{} tuple-type(nth\_tl(n;L)))
Date html generated:
2016_05_14-PM-03_58_37
Last ObjectModification:
2015_12_26-PM-07_21_43
Theory : tuples
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